Independent Researcher, Big06-B-v2, 2026, pp. 1-123
Big06-B: Operational treatment of the dark-matter observational ledger under the Big06-A declaration
Ngo Cheung
Independent Researcher
25 October 2026 (version 1; requests t349u and t350u)
Abstract
Standing non-claims. Host A and Host B stay separate prescribed backgrounds. Host C is not created. O.1 stays NOT_CLOSED. XV-B is not opened. XVI-N is not discharged. Gate 0 and ST4b stay NOT_SUPPLIED. No quantum coefficient is admitted. No Einstein dynamics, derived metric, spacetime emergence, Page curve, island, vacuum energy, or quantized relational time without an external clock is claimed. A source record is not a premise. The OpenAI catalogue is not a premise. Printed numbers are conditional calculations, not measurements. No dark-matter particle species is derived.
Plan-requested line (t355u). No dark-matter particle species is derived.
Version 2 of Big06-B implements, by insertion only, the binding plan of request t355u for this sheet, which replaces the plan of request t354u, and folds in the draft of request t356u (``Big06-B: New Insertion Findings''), whose structure it follows and whose 38 items F15 are re-proved here. Version 1 is retained verbatim below its own abstract; deleting the delimited version-2 blocks returns it byte for byte. New findings. (1) Joint-fibre constancy. Every functional of the metric, its curvature, the declared observers and clocks, and the non-electromagnetic reading, and every adaptive protocol built from them, is constant on the joint fibre of stress-energy splits and current assignments, which is a product. A target is identifiable from such data only if it is constant on that fibre. (2) Relative risk. For the unrestricted dark-to-ordinary ratio the minimax relative risk is exactly 1 under relative absolute or squared loss, attained only by reporting 0. The value stays exact under a common complete process, stopping and postselection on a common event. Under approximate common processes within total variation η the sharp value is 1 − η, not 1, with a two-point bound (b − a)/(b + a)(1 − η), conditioning and stopping budgets, and an endpoint-domination hypothesis that restores exactly 1. A deterministic rule of a fixed datum has risk 1 if it reports 0 and ∞ otherwise. (3) Residual and kernels. The residual is a function of the supply exactly when geometry, coupling, vacuum convention and known sources are all supplied. The residual map is then an affine isometry with no equation of state, and the kernel of the total is exactly the conserved transfers. (4) Poisson layer. Totals, the mass-slope exponent and total shell masses are fibre-constant. The dark slope at a point takes every real value while every dark shell mass of a partition is fixed. The uniform-data discontinuity holds for every topology dominated by the uniform norm, even C¹ convergence of potentials, and Hessian control restores a Lipschitz bound with the sharp constant √(3)/(4πG). The mass-slope constant is 0 in the degenerate class, correcting version 1. A full-aperture virial moment admits a nonnegative residual iff W_d ≥ 0, pins the enclosed mass to exactly [0, W_d/K(R)] and forces mass toward the bound's shell quantitatively. (5) Energy conditions. On a vacuum-form total every split into null-energy-respecting slots is of vacuum type, and a positive dust slot forces the other slots to violate the null energy condition by ε(u · ℓ)² along every null direction. The vacuum shift keeps currents and null contractions. It keeps dust form only at zero shift and the weak energy condition only on a closed interval. At action level it is T ↦ T − Cg with Λ^{′} = Λ − χC, and it is not a residual ambiguity once the other slots are fixed. (6) Futures. On smooth futures that share a past, every rule decides the existence of an event horizon with success at most max {π, 1 − π}, exactly 1/2 at equal prior. The ambiguity survives energy conditions on the total and a supplied positive-dust history. Analytic futures are fixed by the past, and a horizon below c/H costs a null-energy violation. (7) Relations and Shredder. The two forms of the growth diagnostic agree, and an integral form needs no second derivative; slip residuals carry force and calibration terms. The growth and slip relations are independent, each with its own rejection condition. The Shredder floors 1 − 1/d and 1 − 1/d² are constant on the joint fibre, and a replacement channel has error exactly 1 − 1/S with S = ∑ᵢ λᵢ⁻¹ ≥ d². Why it matters. These results separate what the ledger determines (totals, slopes of totals, residuals under full supply, null contractions, access floors) from what remains a coordinate of the split, the current, the vacuum convention or the future. They also state the loss, range, supply or approximation on which each exact constant depends. Audit. Of 29 plan items, 21 are held, 8 are corrected and none is rejected; the withdrawn t354u plan is marked superseded. Of 38 draft items, 36 are held, 2 are corrected, none is rejected and none is a conjecture. The appendices list 18 plan corrections (PB2) and 7 corrections (DC7), three to version 1 and four to the draft. Every label the plan names was confirmed in fresh read-only site records or, for overlay labels, in the local overlay files, and every F13 number and main-finding reference matches version 1. Citations identify source records only; no proof transfer. No quantum coefficient is admitted.
Bibliographic record
- Title
- Big06-B: Operational treatment of the dark-matter observational ledger under the Big06-A declaration
- Author
- Cheung, Ngo
- Affiliation
- Independent Researcher
- Publication date
- 2026
- Institution
- Independent Researcher
- Report number
- Big06-B-v2
- Publisher
- Cheung Ngo Medical Limited
- First page
- 1
- Last page
- 123
- Language
- en